Distance Estimation from WiFi Signal Strength Manhattan Distance Estimation

point clouds. The planar information width, height and the normal direction obtained during the segmentation process is used to classify the point clouds and the ground points can be distinguished and the noisy non-facade points are removed. A sweep plane is used to cut the extracted facade points into a series of small bands of points with constant height of 0.2 meter from bottom to top. Then TLS wall line segments at every 0.2 height level can be obtained. Both floor plan wall and floor plan wall line segments are reconnected using virtual lines and decomposed into small matching units with local transformation invariant features and represented using a line matrix. The adapted normalized cross- correlation function is employed to measure the similarity between the line sequence matrices Equation 1.                                 4 1 1 2 4 1 1 2 4 1 1 i n j ij i n j ij i n j ij ij F F T T F F T T S 1 Where: n = number of columns of T, F 4 = number of rows of T, F T ij = value from matrix T at row i, column j T = average of all digital numbers in T F ij = value from matrix F at row i, column j F = average of all digital numbers in F A group matching algorithm is applied to simultaneously determine final matching results across floor plans and estimate translation and relative orientation vectors between floor plans and TLS station. The floor plans are then georeferenced and registered to the TLS point clouds.

4.2 Integration of 3D Building Modeling With GIS

Database After registration, the horizontal extents and locations of façade features like windows and doors are known. Then a sweep line based method is used to find the façade feature outlines and vertical locations. Based on the detected facade feature locations, 3D façade model and indoor model are reconstructed simultaneously and integrated into one model. Figure 3 shows an example of the reconstructed integrated 3D indoor and facade model. Figure 3. An example of reconstructed integrated 3D building model From floor plans and other administrative databases, indoor GIS can be created and then integrated with existing outdoor GIS to establish a continuous indoor and outdoor GIS system. The GIS system can then be extended to 3D by integrating the 3D building models. First, room polygons are extracted from the floor plans of the PSE building on Keele campus. Then, attributes, like building name, floor number, room number, room owner, room type, etc., are created. The values of these attributes can be extracted from floor plans and administrative database. The dynamic and real-time information like room temperature can also be added to this database. All the information are imported to a PostgreSQLPostGIS database and thus, an indoor building virtual model is established. Because the floor plans were already georeferenced as explained in section 4.1, then the indoor GIS data and existing outdoor GIS data can be seamlessly integrated. After building the seamless indoor and outdoor GIS database, the 3D integrated building models are also stored in it, which are represented and stored using polygons and multipatches. Then, in the end a seamless dynamic 3D GIS database were established.

5. INDOOR POSITION ESTIMATION

The procedure for WiFi-based indoor position estimation is detailed in this section. The indoor position estimation in this study considers result obtained from a sequential two-steps method. First, a deterministic k-NN method using Manhattan distance estimation was applied to provide a preliminary generaliz ation of the person’s location from within a WiFi fingerprint database for the building. This generalization will limit the possible positions of the WiFi user to four locations that are predefined in the database. Then the MAP estimation method will select the most likely position out of the four selected locations by comparing the difference in distance between each estimated location to a pair of known access point locations. The smaller the difference in distance, the higher the likelihood of an accurate estimated position. Distance is obtained by converting received signal strength from nearby access points AP. The purpose of using this hybrid approach is to increase the effectiveness of a coarsely sampled fingerprint map either due to practical urgency needs for deployment or due to a lack of APs to provide a dense enough WiFi coverage to meet an acceptable indoor positioning precision threshold for a certain application.

5.1 Distance Estimation from WiFi Signal Strength

The Log-Distance Path Loss LDPL model is a radio signal propagation model used to estimate path loss of a signal. By using a mathematical model of indoor signal propagation, it can help reduce the dependency on empirical data of the indoor localization algorithm [8]. The model is used to solve the distance d see Equation 2, between a person at an unknown position and the AP location [2]. logd 10n + S = S 1m 2 Where: S = signal path loss between AP and receiver S 1m = signal path loss at 1 meter away from AP d = distance in meter between receiver and AP n = path loss exponent of the environment

5.2 Manhattan Distance Estimation

K-nearest neighbour k-NN classification is a simple machine learning algorithm that classifies objects based on distance andor similarity measure. With data points positioned in an input space, the objective of k-NN is to determine which training data are close to it. The function of k-NN is to approximate the data points, the WiFi signal strength measurements in our context, to the closest samples, the pre-recorded data stored in the fingerprint database. It accomplishes this by computing the distance to each data point in the training set using distance estimation methods such as Manhattan distance estimation. Manhattan distance estimation is to determine the closeness of the data points to the sample data as described in equation 3. In ISPRS Acquisition and Modelling of Indoor and Enclosed Environments 2013, 11 – 13 December 2013, Cape Town, South Africa This contribution has been peer-reviewed. doi:10.5194isprsarchives-XL-4-W4-1-2013 4 this method, the distance between two points is computed in signal space. The points can be represented by the real-time WiFi signal strength measurement of a person and the signal strength pre-recorded in the WiFi fingerprint database. According to [6], if the database contain M fingerprints and has a set of locations define as L = { l 1 , l 2 , l 3 , ..., l k }, then to calculate the location represented by a set of received signal strengths RSSI 1 , RSSI 2 , …, RSSI n , we can define the problem as follow: For each l ϵ 1,…, M calculate the minimum distance �̂ � between � , � , ..., � and � � , � � , …, � � Where: l denotes a location u denotes a user location n denotes no. measurements available at location u � is the signal strength in database from i -th AP � � is the observed signal strength � 4 � is a set of four locations closest to the person �̂ � = ∑ | � = − � � | 3 � 4 � = arg kmin =4; 4 ϵ �̂ � 4 Upon calculating the minimum distances for all locations in the fingerprint database, equation 4 will be used to infer the top four locations based on their �̂ � .

5.3 Maximum a Posteriori Estimation